Bifurcations and Chaos in Voice Signals

1993 ◽  
Vol 46 (7) ◽  
pp. 399-413 ◽  
Author(s):  
Hanspeter Herzel
Keyword(s):  
Early Diagnosis ◽  
Speech Production ◽  
Deterministic Chaos ◽  
Brain Disorder ◽  
Poincaré Sections ◽  
Physical Mechanisms ◽  
Rich Variety ◽  
Low Dimensional ◽  
Poincare Sections

The basic physical mechanisms of speech production is described. A rich variety of bifurcations and episodes of irregular behaviour are observed. Poincare´ sections and the analysis of the underlying attractor suggest that these noise-like episodes are low-dimensional deterministic chaos. Possible implications for the very early diagnosis of brain disorder are discussed.

scholarly journals Scaling and universality in the human voice

2015 ◽  
Vol 12 (105) ◽  
pp. 20141344 ◽  
Author(s):  
Jordi Luque ◽  
Bartolo Luque ◽  
Lucas Lacasa
Keyword(s):  
Speech Production ◽  
Power Law ◽  
Speech Processing ◽  
Speech Synthesis ◽  
Deterministic Chaos ◽  
Scale Invariant ◽  
Human Capabilities ◽  
Human Speech ◽  
Temporal Correlations ◽  
Low Dimensional

Speech is a distinctive complex feature of human capabilities. In order to understand the physics underlying speech production, in this work, we empirically analyse the statistics of large human speech datasets ranging several languages. We first show that during speech, the energy is unevenly released and power-law distributed, reporting a universal robust Gutenberg–Richter-like law in speech. We further show that such ‘earthquakes in speech’ show temporal correlations, as the interevent statistics are again power-law distributed. As this feature takes place in the intraphoneme range, we conjecture that the process responsible for this complex phenomenon is not cognitive, but it resides in the physiological (mechanical) mechanisms of speech production. Moreover, we show that these waiting time distributions are scale invariant under a renormalization group transformation, suggesting that the process of speech generation is indeed operating close to a critical point. These results are put in contrast with current paradigms in speech processing, which point towards low dimensional deterministic chaos as the origin of nonlinear traits in speech fluctuations. As these latter fluctuations are indeed the aspects that humanize synthetic speech, these findings may have an impact in future speech synthesis technologies. Results are robust and independent of the communication language or the number of speakers, pointing towards a universal pattern and yet another hint of complexity in human speech.

scholarly journals Classifying the Epilepsy Based on the Phase Space Sorted With the Radial Poincaré Sections in Electroencephalography

2021 ◽  
Vol 7 (2) ◽  
pp. 60-73
Author(s):  
Reyhaneh Zarifiyan Irani Nezhad ◽  
◽  
Ghasem Sadeghi Bajestani ◽  
Reza Yaghoobi Karimui ◽  
Behnaz Sheikholeslami1 ◽  
...  
Keyword(s):  
Phase Space ◽  
Brain Activity ◽  
Epileptic Seizures ◽  
Computational Method ◽  
Statistical Characteristics ◽  
Support Vector ◽  
Brain Disorder ◽  
Poincaré Sections ◽  
Significant Difference ◽  
Poincare Sections

Background: Epilepsy is a brain disorder that changes the basin geometry of the oscillation of trajectories in the phase space. Nevertheless, recent studies on epilepsy often used the statistical characteristics of this space to diagnose epileptic seizures. Objectives: We evaluated changes caused by the seizures on the mentioned basin by focusing on phase space sorted by Poincaré sections. Materials & Methods: In this non-interventional clinical study (observational), 19 patients with generalized epilepsy were referred to the Epilepsy Department of Razavi Hospital (Mashhad, Iran) between 2018 and 2020, which their disease had been controlled after diagnosis and surgery. In evaluating the effects of this disorder on the oscillation basin of the EEG trajectories, we used the MATLAB@ R2019 software. In this computational method, we sorted the phase space reconstructed from the trajectories by using the radial Poincaré sections and then extracted a set of the geometric features. Finally, we detected the normal, pre-ictal, and ictal modes using a decision tree based on the Support Vector Machine (SVM) developed by features selected by a genetic algorithm. Results: The proposed method provided an accuracy of 94.96% for the three classes, which confirms the change in the oscillation basin of the trajectories. Analyzing the features by using t test also showed a significant difference between the three modes. Conclusion: The findings prove that epilepsy increases the oscillations basin of brain activity, but classification based on the segment cannot be applicable in clinical settings.

Hamiltonian Chaos in a Model Alveolus

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
F. S. Henry ◽  
F. E. Laine-Pearson ◽  
A. Tsuda
Keyword(s):  
Reynolds Number ◽  
Fixed Point ◽  
Lyapunov Exponent ◽  
Fine Particles ◽  
Hamiltonian Dynamics ◽  
Maximal Lyapunov Exponent ◽  
Poincaré Sections ◽  
Pulmonary Acinus ◽  
Hamiltonian Chaos ◽  
Poincare Sections

In the pulmonary acinus, the airflow Reynolds number is usually much less than unity and hence the flow might be expected to be reversible. However, this does not appear to be the case as a significant portion of the fine particles that reach the acinus remains there after exhalation. We believe that this irreversibility is at large a result of chaotic mixing in the alveoli of the acinar airways. To test this hypothesis, we solved numerically the equations for incompressible, pulsatile, flow in a rigid alveolated duct and tracked numerous fluid particles over many breathing cycles. The resulting Poincaré sections exhibit chains of islands on which particles travel. In the region between these chains of islands, some particles move chaotically. The presence of chaos is supported by the results of an estimate of the maximal Lyapunov exponent. It is shown that the streamfunction equation for this flow may be written in the form of a Hamiltonian system and that an expansion of this equation captures all the essential features of the Poincaré sections. Elements of Kolmogorov–Arnol’d–Moser theory, the Poincaré–Birkhoff fixed-point theorem, and associated Hamiltonian dynamics theory are then employed to confirm the existence of chaos in the flow in a rigid alveolated duct.

Perturbing variables in poincaré sections to suppress chaos

2008 ◽  
pp. 339-340
Author(s):  
J. M. Gutiérrez ◽  
A. Iglesias ◽  
J. Güémez ◽  
M. A. Matías
Keyword(s):  
Poincaré Sections ◽  
Poincare Sections

scholarly journals Deterministic Chaos in the Microstructure of Radio Pulses of PSR 0809+74

1992 ◽  
Vol 128 ◽  
pp. 329-331
Author(s):  
V. I. Zhuravlev ◽  
M. V. Popov
Keyword(s):  
Radio Emission ◽  
Random Sequence ◽  
Nonlinear Dynamical System ◽  
Deterministic Chaos ◽  
Relativistic Plasma ◽  
Emission Region ◽  
Polar Cap ◽  
Nonlinear Dynamical ◽  
Developed Turbulence ◽  
Low Dimensional

Abstract480 single pulses from PSR 0809+74, recorded at 102.5 MHz with a time resolution of 10μs, have been analyzed by the time delay technique in order to look for the parameters of deterministic chaos in the microstructure of radio pulses. The correlation dimension n was shown to be less than 5 in more than 20% of the analyzed pulses. This means that on such occasions the microstructure of pulsar radio emission with the time scales 10 to 100μs may be determined by the behavior of a nonlinear dynamical system with comparatively small numbers of independent parameters. For example, the observed low dimensional chaos may result from a turbulence process associated with the outflow of plasma—as in versions of the polar cap model where microstructure can be interpreted as reflecting the spatial structure of relativistic plasma outflow in the radio emission region.However, the correlation-time distribution demonstrates the tendency for microstructure to consist of a random sequence of unresolved micropulses in the majority of cases, which means in the framework of polar cap models the presence of well developed turbulence in the relativistic plasma outflow.

Simultaneous Resonances of Suspended Cables Subjected to Primary and Super-Harmonic Excitations in Thermal Environments

2019 ◽  
Vol 19 (12) ◽  
pp. 1950155
Author(s):  
Yaobing Zhao ◽  
Henghui Lin ◽  
Lincong Chen ◽  
Chenfei Wang
Keyword(s):  
Perturbation Method ◽  
Multiple Scales ◽  
Effect Of Temperature ◽  
Response Curves ◽  
Temperature Changes ◽  
Poincaré Sections ◽  
Thermal Environments ◽  
Direct Integration Method ◽  
Harmonic Excitations ◽  
Poincare Sections

This paper concerns with a suspended cable in thermal environments under bi-frequency harmonic excitations, with a focus placed on the effect of temperature changes on one type of simultaneous resonance. First, the nonlinear equation of motion in thermal environments is obtained for the in-plane displacement of the cable. Then, the Galerkin method is employed to reduce the partial differential equation to an ordinary one. Second, based on the discretized form of the governing equation, the method of multiple scales is employed to obtain the second-order approximate solutions, with the stability characteristics determined. Third, numerical results are presented by using the perturbation method, together with numerical integration by the following means: frequency-response curves, time-displacement curves, phase-plane diagrams, and Poincare sections. The direct integration method is utilized to verify the results obtained by the perturbation method, while revealing more nonlinear dynamic behaviors induced by temperature changes. Both the softening and/or hardening behaviors, and the switching between them are observed for the cable in thermal environments. The response amplitude of the cable is very sensitive to temperature changes, but the number of circles in the phase diagrams and the number of cluster points in Poincaré sections is independent of the thermal effects in most cases. Finally, the vibration characteristics of the cable for different thermal expansion coefficients and temperature-dependent Young’s moduli are also investigated.

scholarly journals Nonlinear dynamics and Poincaré sections to model gait impairments in different stages of Parkinson’s disease

2020 ◽  
Vol 100 (4) ◽  
pp. 3253-3276
Author(s):  
P. A. Pérez-Toro ◽  
J. C. Vásquez-Correa ◽  
T. Arias-Vergara ◽  
E. Nöth ◽  
J. R. Orozco-Arroyave
Keyword(s):  
Nonlinear Dynamics ◽  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Poincaré Sections ◽  
Poincare Sections ◽  
Gait Impairments

Chaotic Motion of a Parametrically Excited Dielectric Elastomer

2020 ◽  
Vol 12 (03) ◽  
pp. 2050033
Author(s):  
Hamidreza Heidari ◽  
Amin Alibakhshi ◽  
Habib Ramezannejad Azarboni
Keyword(s):  
Time Integration ◽  
Nonlinear Behavior ◽  
Strain Energy Function ◽  
Nonlinear Ordinary Differential Equation ◽  
Dielectric Elastomer ◽  
Dissipation Function ◽  
Bifurcation Diagrams ◽  
Chaotic Motions ◽  
Poincaré Sections ◽  
Poincare Sections

In this paper, an effort is made to study the chaotic motions of a dielectric elastomer (DE). The DE is activated by a time-dependent voltage (AC voltage), which is superimposed on a DC voltage. The Gent strain energy function is employed to model the nonlinear behavior of the elastomeric matter. The nonlinear ordinary differential equation (ODE) in terms of the stretch of the elastomer governing the motion of the system is deduced using the Euler–Lagrange method and the Rayleigh dissipation function. This ODE is solved via the use of a time integration-based solver. The bifurcation diagrams of Poincaré sections are generated to identify the chaotic domains. The largest Lyapunov exponents (LLEs) are illustrated for validation of the results obtained by the bifurcation diagrams. Various types of motion for the system are precisely discussed through the depiction of stretch-time responses, phase-plane diagrams, Poincaré sections and power spectral density (PSD) diagrams. The results reveal that the damping coefficient plays an influential role in suppressing the chaos phenomenon. Besides, the initial stretch of the elastomer could affect the chaotic interval of system parameters.

scholarly journals Poincaré sections of Hamiltonian systems

1996 ◽  
Vol 95 (2-3) ◽  
pp. 171-189 ◽  
Author(s):  
E.S. Cheb-Terrab ◽  
H.P. de Oliveira
Keyword(s):  
Hamiltonian Systems ◽  
Poincaré Sections ◽  
Poincare Sections

Global Dynamics of an Autoparametric System With Multiple Pendulums

2005 ◽  
Vol 1 (1) ◽  
pp. 35-46 ◽  
Author(s):  
Ashwin Vyas ◽  
Anil K. Bajaj
Keyword(s):  
Initial Conditions ◽  
Hamiltonian Formulation ◽  
Forced Response ◽  
Global Dynamics ◽  
Equilibrium Solutions ◽  
External Excitation ◽  
Poincaré Sections ◽  
Poincare Sections ◽  
Hamilton's Equations ◽  
Hamilton’S Equations

The Hamiltonian dynamics of a resonantly excited linear spring-mass-damper system coupled to an array of pendulums is investigated in this study under 1:1:1:…:2 internal resonance between the pendulums and the linear oscillator. To study the small-amplitude global dynamics, a Hamiltonian formulation is introduced using generalized coordinates and momenta, and action-angle coordinates. The Hamilton’s equations are averaged to obtain equations for the first-order approximations to free and forced response of the system. Equilibrium solutions of the averaged Hamilton’s equations in action-angle or comoving variables are determined and studied for their stability characteristics. The system with one pendulum is known to be integrable in the absence of damping and external excitation. Exciting the system with even a small harmonic forcing near a saddle point leads to stochastic response, as clearly demonstrated by the Poincaré sections of motion. Poincaré sections are also computed for motions started with initial conditions near center-center, center-saddle and saddle-saddle-type equilibria for systems with two, three and four pendulums. In case of the system with more than one pendulum, even the free undamped dynamics exhibits irregular exchange of energy between the pendulums and the block. The increase in complexity is also demonstrated as the number of pendulums is increased, and when external excitation is present.

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